Senate Majority Leader Harry Reid (right) of Nevada gets a pat on the back by Sen. Charles Schumer, D-N.Y., a lead author of the Senate's immigration reform bill, as Reid arrives to update reporters on the status of the legislation following a Democratic strategy session on Capitol Hill in Washington. (ASSOCIATED PRESS / J. Scott Applewhite)

WASHINGTON (AP) — Sweeping U.S. immigration legislation cruised toward passage in the Senate on Wednesday, but Republicans in the House of Representatives pursued a different approach that cracks down on millions living in the United States illegally rather than offering them a chance at citizenship.

Presidential politics took a more prominent role as Sen. Marco Rubio, a Republican and potential 2016 White House contender, tried to reassure fellow conservatives that many criticisms of the Senate bill, which he helped write in a rare bipartisan effort, are “just not true.”

The White House-backed Senate bill was on track for passage by Thursday or Friday. President Barack Obama would like to have an immigration bill passed by Congress so he can point to a major legislative success in the first year of his second term.

Immigration is one area in which both major political parties have managed to find common ground in a bitterly divisive Congress. Republicans turned to immigration reform after losing badly in last year’s presidential election as Obama benefited from a growing Hispanic vote.

The Senate legislation includes numerous steps to prevent future illegal immigration, while offering a chance at citizenship for millions living in the country illegally.

It provides for 20,000 new Border Patrol agents, requires the completion of 700 miles (1,226 kilometers) of fencing along the border with Mexico and requires an array of high-tech devices be deployed to secure that border.

Businesses would be required to check on the legal status of prospective employees. The government would be ordered to install a high-tech system to check on the comings and goings of foreigners at selected international airports in the United States.

Other provisions would expand the number of visas for highly skilled workers relied upon by the technology industry. A separate program would be established for lower-skilled workers, and farm workers would be admitted under a temporary program.

The legislation was drafted by four Democrats and four Republicans who met privately for months to produce a rare bipartisan compromise.

In the House, an attempt at a bipartisan deal faltered, and majority Republicans began moving ahead on legislation tailored to the wishes of conservatives and vehemently opposed by Obama’s Democrats.

One of the bills approved by the House Judiciary Committee makes it a new crime to remain in the country without legal status. It also allows state and local governments to enforce federal immigration laws, an attempt to apprehend more immigrants living in the United States illegally. It encourages those living in the United States unlawfully to depart voluntarily.

With attention beginning to shift to the House, Rep. John Fleming said House Speaker John Boehner, a fellow Republican, had assured party members they will vote on bills being written in the House.

“We are not going to take up the Senate bill,” Fleming said, quoting the speaker.